arXiv subjects

Michael Hoffmann

Publications and source records attributed to Michael Hoffmann.

At least 19 recordsLinked to original sources

arXiv2026

BavGround: A Benchmark for Regional Cultural Grounding and Dialect Competence in Bavarian

Cultural evaluation of large language models (LLMs) often focuses on high-resource standard languages, leaving regional culture and dialect communities underrepresented. We introduce BavGround, a benchmark for evaluating Bavarian regional cultural grounding and dialect competence across English, German and Bavarian. BavGround contains 206 multiple-choice source questions across eight cultural domains per language, yielding 618 multi-parallel instances, with items covering both broadly accessible cultural knowledge and source-grounded regional knowledge from journalism, historical sources, and specialist literature. We evaluate fifteen 7B-10B open-weight instruction-tuned models and one closed-model reference. Strong multilingual models perform best overall, but performance drops on Bavarian items and source-grounded questions, indicating persistent difficulty with dialectal and localized cultural knowledge. We further show that conclusions depend strongly on evaluation protocol: raw answer-letter scoring, shuffled-letter scoring, option-text likelihood, generated-answer parsing, and semantic matching can produce different absolute scores and rankings, especially for regionally adapted models. Finally, an exploratory analysis of GENBA-10B checkpoints suggests that continued pretraining improves answer-content likelihood unevenly across domains, while dialect competence remains comparatively weak. BavGround supports localized, protocol-aware evaluation of cultural representation in LLMs.

cs.CL↗

arXiv2026

Weighted Book Thickness

We introduce and study the weighted book thickness of graphs. A $k$-page book embedding of a graph $G=(V,E)$ is defined by a spanning cycle $C$ for $V$ (which does not need to be part of $G$) and a partition $E=\bigcup_{i=1}^{k}E_i$ such that $E\cap C\subseteq E_1$ and each graph $G_i=(V,E_i\cup C)$, for $1 \le i \le k$, is outerplane with outer cycle $C$. If $e\in E_i$, we say that $e$ appears on Page $i$. The classical book thickness of a graph $G$ is the minimum $k$ such that there exists a $k$-page book embedding of $G$, that is, the minimum (over all book embeddings of $G$) achievable maximum page an edge appears on. In contrast, the weighted book thickness is the minimum achievable average page an edge appears on. The embeddings that realize weighted book thickness can differ from those that realize (classical) book thickness. We show that, although every planar graph on at most nine vertices admits a 2-page book embedding realizing its weighted book thickness, already for ten vertices, there is a planar graph for which every realization of its weighted book thickness needs more pages than its book thickness. We prove that there even exists a 2-tree whose weighted book thickness cannot be realized on two pages. On the positive side, we show that for every graph of pathwidth at most two, the weighted book thickness can always be realized by a 2-page book embedding and such an embedding can be found in linear time. Moreover, we prove that it is NP-complete to decide if the weighted book thickness is at most $k$, for some given integer $k$.

cs.CG↗

arXiv2026

A Gray code for arborescences of tournaments

We consider the following question of Knuth: given a directed graph $G$ and a root $r$, can the arborescences of $G$ rooted in $r$ be listed such that any two consecutive arborescences differ by only one arc? Such an ordering is called a pivot Gray code and can be formulated as a Hamiltonian path in the reconfiguration graph of the arborescences of $G$ under arc flips, also called flip graph of $G$. We give a positive answer for tournaments and explore several conditions showing that the flip graph of a directed graph may contain no Hamiltonian cycles.

math.CO↗

arXiv2025

Designing and Evaluating Malinowski's Lens: An AI-Native Educational Game for Ethnographic Learning

This study introduces 'Malinowski's Lens', the first AI-native educational game for anthropology that transforms Bronislaw Malinowski's 'Argonauts of the Western Pacific' (1922) into an interactive learning experience. The system combines Retrieval-Augmented Generation with DALL-E 3 text-to-image generation, creating consistent VGA-style visuals as players embody Malinowski during his Trobriand Islands fieldwork (1915-1918). To address ethical concerns, indigenous peoples appear as silhouettes while Malinowski is detailed, prompting reflection on anthropological representation. Two validation studies confirmed effectiveness: Study 1 with 10 non-specialists showed strong learning outcomes (average quiz score 7.5/10) and excellent usability (SUS: 83/100). Study 2 with 4 expert anthropologists confirmed pedagogical value, with one senior researcher discovering "new aspects" of Malinowski's work through gameplay. The findings demonstrate that AI-driven educational games can effectively convey complex anthropological concepts while sparking disciplinary curiosity. This study advances AI-native educational game design and provides a replicable model for transforming academic texts into engaging interactive experiences.

cs.HC↗

arXiv2025

Llama-GENBA-10B: A Trilingual Large Language Model for German, English and Bavarian

We present Llama-GENBA-10B, a trilingual foundation model addressing English-centric bias in large language models. Built on Llama 3.1-8B and scaled to 10B parameters, Llama-GENBA-10B is continuously pretrained on 164B tokens (82B English, 82B German, and 80M Bavarian), balancing resources while preventing English dominance. Targeted at the German NLP community, the model also promotes Bavarian as a low-resource language. Development tackled four challenges: (1) curating a multilingual corpus despite Bavarian scarcity, (2) creating a unified tokenizer for English, German, and Bavarian, (3) optimizing architecture and language-ratio hyperparameters for cross-lingual transfer, and (4) establishing the first standardized trilingual evaluation suite by translating German benchmarks into Bavarian. Evaluations show that Llama-GENBA-10B achieves strong cross-lingual performance, with the fine-tuned variant surpassing Apertus-8B-2509 and gemma-2-9b in Bavarian and establishing itself as the best model in its class for this language, while also outperforming EuroLLM in English and matching its results in German. Training on the Cerebras CS-2 demonstrated efficient large-scale multilingual pretraining with documented energy use, offering a blueprint for inclusive foundation models that integrate low-resource languages.

cs.CL↗

arXiv2025

Crossing Number of 3-Plane Drawings

We study 3-plane drawings, that is, drawings of graphs in which every edge has at most three crossings. We show how the recently developed Density Formula for topological drawings of graphs (KKKRSU GD 2024) can be used to count the crossings in terms of the number $n$ of vertices. As a main result, we show that every 3-plane drawing has at most $5.5(n-2)$ crossings, which is tight. In particular, it follows that every 3-planar graph on $n$ vertices has crossing number at most $5.5n$, which improves upon a recent bound (BBBDHKMOW GD 2024) of $6.6n$. To apply the Density Formula, we carefully analyze the interplay between certain configurations of cells in a 3-plane drawing. As a by-product, we also obtain an alternative proof for the known statement that every 3-planar graph has at most $5.5(n-2)$ edges.

math.CO↗

arXiv2025

Geometric realizations of dichotomous ordinal graphs

A dichotomous ordinal graph consists of an undirected graph with a partition of the edges into short and long edges. A geometric realization of a dichotomous ordinal graph $G$ in a metric space $X$ is a drawing of $G$ in $X$ in which every long edge is strictly longer than every short edge. We call a graph $G$ pandichotomous in $X$ if $G$ admits a geometric realization in $X$ for every partition of its edge set into short and long edges. We exhibit a very close relationship between the degeneracy of a graph $G$ and its pandichotomic Euclidean or spherical dimension, that is, the smallest dimension $k$ such that $G$ is pandichotomous in $\mathbb{R}^k$ or the sphere $\mathbb{S}^k$, respectively. First, every $d$-degenerate graph is pandichotomous in $\mathbb{R}^{d}$ and $\mathbb{S}^{d-1}$ and these bounds are tight for the sphere and for $\mathbb{R}^2$ and almost tight for $\mathbb{R}^d$, for $d\ge 3$. Second, every $n$-vertex graph that is pandichotomous in $\mathbb{R}^k$ has at most $\mu kn$ edges, for some absolute constant $\mu<7.23$. This shows that the pandichotomic Euclidean dimension of any graph is linearly tied to its degeneracy and in the special cases $k\in \{1,2\}$ resolves open problems posed by Alam, Kobourov, Pupyrev, and Toeniskoetter. Further, we characterize which complete bipartite graphs are pandichotomous in $\mathbb{R}^2$: These are exactly the $K_{m,n}$ with $m\le 3$ or $m=4$ and $n\le 6$. For general bipartite graphs, we can guarantee realizations in $\mathbb{R}^2$ if the short or the long subgraph is constrained: namely if the short subgraph is outerplanar or a subgraph of a rectangular grid, or if the long subgraph forms a caterpillar.

cs.CG↗

arXiv2025

ParkView: Visualizing Monotone Interleavings

Merge trees are a powerful tool from topological data analysis that is frequently used to analyze scalar fields. The similarity between two merge trees can be captured by an interleaving: a pair of maps between the trees that jointly preserve ancestor relations in the trees. Interleavings can have a complex structure; visualizing them requires a sense of (drawing) order which is not inherent in this purely topological concept. However, in practice it is often desirable to introduce additional geometric constraints, which leads to variants such as labeled or monotone interleavings. Monotone interleavings respect a given order on the leaves of the merge trees and hence have the potential to be visualized in a clear and comprehensive manner. In this paper, we introduce ParkView: a schematic, scalable encoding for monotone interleavings. ParkView captures both maps of the interleaving using an optimal decomposition of both trees into paths and corresponding branches. We prove several structural properties of monotone interleavings, which support a sparse visual encoding using active paths and hedges that can be linked using a maximum of 6 colors for merge trees of arbitrary size. We show how to compute an optimal path-branch decomposition in linear time and illustrate ParkView on a number of real-world datasets.

cs.CG↗

arXiv2024

On $k$-planar Graphs without Short Cycles

We study the impact of forbidding short cycles to the edge density of $k$-planar graphs; a $k$-planar graph is one that can be drawn in the plane with at most $k$ crossings per edge. Specifically, we consider three settings, according to which the forbidden substructures are $3$-cycles, $4$-cycles or both of them (i.e., girth $\ge 5$). For all three settings and all $k\in\{1,2,3\}$, we present lower and upper bounds on the maximum number of edges in any $k$-planar graph on $n$ vertices. Our bounds are of the form $c\,n$, for some explicit constant $c$ that depends on $k$ and on the setting. For general $k \geq 4$ our bounds are of the form $c\sqrt{k}n$, for some explicit constant $c$. These results are obtained by leveraging different techniques, such as the discharging method, the recently introduced density formula for non-planar graphs, and new upper bounds for the crossing number of $2$-- and $3$-planar graphs in combination with corresponding lower bounds based on the Crossing Lemma.

math.CO↗

arXiv2024

Monotone Arc Diagrams with few Biarcs

We show that every planar graph has a monotone topological 2-page book embedding where at most (4n-10)/5 (of potentially 3n-6) edges cross the spine, and every edge crosses the spine at most once; such an edge is called a biarc. We can also guarantee that all edges that cross the spine cross it in the same direction (e.g., from bottom to top). For planar 3-trees we can further improve the bound to (3n-9)/4, and for so-called Kleetopes we obtain a bound of at most (n-8)/3 edges that cross the spine. The bound for Kleetopes is tight, even if the drawing is not required to be monotone. A Kleetope is a plane triangulation that is derived from another plane triangulation T by inserting a new vertex v_f into each face f of T and then connecting v_f to the three vertices of f.

cs.DM↗

arXiv2024

Report on the Conference on Ethical and Responsible Design in the National AI Institutes: A Summary of Challenges

In May 2023, the Georgia Tech Ethics, Technology, and Human Interaction Center organized the Conference on Ethical and Responsible Design in the National AI Institutes. Representatives from the National AI Research Institutes that had been established as of January 2023 were invited to attend; researchers representing 14 Institutes attended and participated. The conference focused on three questions: What are the main challenges that the National AI Institutes are facing with regard to the responsible design of AI systems? What are promising lines of inquiry to address these challenges? What are possible points of collaboration? Over the course of the conference, a revised version of the first question became a focal point: What are the challenges that the Institutes face in identifying ethical and responsible design practices and in implementing them in the AI development process? This document summarizes the challenges that representatives from the Institutes in attendance highlighted.

cs.CY↗

arXiv2024

3D ferroelectric phase field simulations of polycrystalline multi-phase hafnia and zirconia based ultra-thin films

HfO$_2$- and ZrO$_2$-based ferroelectric thin films have emerged as promising candidates for the gate oxides of next generation electronic devices. Recent work has experimentally demonstrated that a tetragonal/orthorhombic (t/o-) phase mixture with partially in-plane polarization can lead to negative capacitance (NC) stabilization. However, there is a discrepancy between experiments and the theoretical understanding of domain formation and domain wall motion in these multi-phase, polycrystalline materials. Furthermore, the effect of anisotropic domain wall coupling on NC has not been studied so far. Here we apply 3D phase field simulations of HfO$_2$- and ZrO$_2$-based mixed-phase ultra-thin films on silicon to understand the necessary and beneficial conditions for NC stabilization. We find that smaller ferroelectric grains and a larger angle of the polar axis with respect to the out-of-plane direction enhances the NC effect. Furthermore, we show that theoretically predicted negative domain wall coupling even along only one axis prevents NC stabilization. Therefore, we conclude that topological domain walls play a critical role in experimentally observed NC phenomena in HfO$_2$- and ZrO$_2$-based ferroelectrics.

cond-mat.mes-hall↗

arXiv2024

Recognition of Unit Segment and Polyline Graphs is $\exists\mathbb{R}$-Complete

Given a set of objects $O$ in the plane, the corresponding intersection graph is defined as follows. Each object defines a vertex and an edge joins two vertices whenever the corresponding objects intersect. We study here the case of unit segments and polylines with exactly $k$ bends. In the recognition problem, we are given a graph and want to decide whether the graph can be represented as an intersection graph of certain geometric objects. In previous work it was shown that various recognition problems are $\exists\mathbb{R}$-complete, leaving unit segments and polylines among the few remaining natural cases where the recognition complexity remained open. We show that recognition for both families of objects is $\exists\mathbb{R}$-complete.

cs.CG↗

arXiv2023

The Number of Edges in Maximal 2-planar Graphs

A graph is $2$-planar if it has local crossing number two, that is, it can be drawn in the plane such that every edge has at most two crossings. A graph is maximal $2$-planar if no edge can be added such that the resulting graph remains $2$-planar. A $2$-planar graph on $n$ vertices has at most $5n-10$ edges, and some (maximal) $2$-planar graphs -- referred to as optimal $2$-planar -- achieve this bound. However, in strong contrast to maximal planar graphs, a maximal $2$-planar graph may have fewer than the maximum possible number of edges. In this paper, we determine the minimum edge density of maximal $2$-planar graphs by proving that every maximal $2$-planar graph on $n\ge 5$ vertices has at least $2n$ edges. We also show that this bound is tight, up to an additive constant. The lower bound is based on an analysis of the degree distribution in specific classes of drawings of the graph. The upper bound construction is verified by carefully exploring the space of admissible drawings using computer support.

math.CO↗

arXiv2023

Drawings of Complete Multipartite Graphs Up to Triangle Flips

For a drawing of a labeled graph, the rotation of a vertex or crossing is the cyclic order of its incident edges, represented by the labels of their other endpoints. The extended rotation system (ERS) of the drawing is the collection of the rotations of all vertices and crossings. A drawing is simple if each pair of edges has at most one common point. Gioan's Theorem states that for any two simple drawings of the complete graph $K_n$ with the same crossing edge pairs, one drawing can be transformed into the other by a sequence of triangle flips (a.k.a. Reidemeister moves of Type 3). This operation refers to the act of moving one edge of a triangular cell formed by three pairwise crossing edges over the opposite crossing of the cell, via a local transformation. We investigate to what extent Gioan-type theorems can be obtained for wider classes of graphs. A necessary (but in general not sufficient) condition for two drawings of a graph to be transformable into each other by a sequence of triangle flips is that they have the same ERS. As our main result, we show that for the large class of complete multipartite graphs, this necessary condition is in fact also sufficient. We present two different proofs of this result, one of which is shorter, while the other one yields a polynomial time algorithm for which the number of needed triangle flips for graphs on $n$ vertices is bounded by $O(n^{16})$. The latter proof uses a Carath\'eodory-type theorem for simple drawings of complete multipartite graphs, which we believe to be of independent interest. Moreover, we show that our Gioan-type theorem for complete multipartite graphs is essentially tight in the sense that having the same ERS does not remain sufficient when removing or adding very few edges.

cs.CG↗

arXiv2022

Bounding and computing obstacle numbers of graphs

An obstacle representation of a graph $G$ consists of a set of pairwise disjoint simply-connected closed regions and a one-to-one mapping of the vertices of $G$ to points such that two vertices are adjacent in $G$ if and only if the line segment connecting the two corresponding points does not intersect any obstacle. The obstacle number of a graph is the smallest number of obstacles in an obstacle representation of the graph in the plane such that all obstacles are simple polygons. It is known that the obstacle number of each $n$-vertex graph is $O(n \log n)$ [Balko, Cibulka, and Valtr, 2018] and that there are $n$-vertex graphs whose obstacle number is $\Omega(n/(\log\log n)^2)$ [Dujmovi\'c and Morin, 2015]. We improve this lower bound to $\Omega(n/\log\log n)$ for simple polygons and to $\Omega(n)$ for convex polygons. To obtain these stronger bounds, we improve known estimates on the number of $n$-vertex graphs with bounded obstacle number, solving a conjecture by Dujmovi\'c and Morin. We also show that if the drawing of some $n$-vertex graph is given as part of the input, then for some drawings $\Omega(n^2)$ obstacles are required to turn them into an obstacle representation of the graph. Our bounds are asymptotically tight in several instances. We complement these combinatorial bounds by two complexity results. First, we show that computing the obstacle number of a graph $G$ is fixed-parameter tractable in the vertex cover number of $G$. Second, we show that, given a graph $G$ and a simple polygon $P$, it is NP-hard to decide whether $G$ admits an obstacle representation using $P$ as the only obstacle.

cs.CG↗

arXiv2021

Hafnia-based Double Layer Ferroelectric Tunnel Junctions as Artificial Synapses for Neuromorphic Computing

Ferroelectric tunnel junctions (FTJ) based on hafnium zirconium oxide (Hf1-xZrxO2; HZO) are a promising candidate for future applications, such as low-power memories and neuromorphic computing. The tunneling electroresistance (TER) is tunable through the polarization state of the HZO film. To circumvent the challenge of fabricating thin ferroelectric HZO layers in the tunneling range of 1-3 nm range, ferroelectric/dielectric double layer sandwiched between two symmetric metal electrodes are used. Due to the decoupling of the ferroelectric polarization storage layer and a dielectric tunneling layer with a higher bandgap, a significant TER ratio between the two polarization states is obtained. By exploiting previously reported switching behaviour and the gradual tunability of the resistance, FTJs can be used as potential candidates for the emulation of synapses for neuromorphic computing in spiking neural networks. The implementation of two major components of a synapse are shown: long term depression/potentiation by varying the amplitude/width/number of voltage pulses applied to the artificial FTJ synapse, and spike-timing-dependent-plasticity curves by applying time-delayed voltages at each electrode. These experimental findings show the potential of spiking neural networks and neuromorphic computing that can be implemented with hafnia-based FTJs.

physics.app-ph↗

arXiv2021

Antiferroelectric negative capacitance from a structural phase transition in zirconia

Crystalline materials with broken inversion symmetry can exhibit a spontaneous electric polarization, which originates from a microscopic electric dipole moment. Long-range polar or anti-polar order of such permanent dipoles gives rise to ferroelectricity or antiferroelectricity, respectively. However, the recently discovered antiferroelectrics of fluorite structure (HfO$_2$ and ZrO$_2$) are different: A non-polar phase transforms into a polar phase by spontaneous inversion symmetry breaking upon the application of an electric field. Here, we show that this structural transition in antiferroelectric ZrO$_2$ gives rise to a negative capacitance, which is promising for overcoming the fundamental limits of energy efficiency in electronics. Our findings provide insight into the thermodynamically 'forbidden' region of the antiferroelectric transition in ZrO$_2$ and extend the concept of negative capacitance beyond ferroelectricity. This shows that negative capacitance is a more general phenomenon than previously thought and can be expected in a much broader range of materials exhibiting structural phase transitions.

cond-mat.mtrl-sci↗